Ambiguous model learning made unambiguous with 1/f priors

What happens to the optimal interpretation of noisy data when there exists more than one equally plausible interpretation of the data? In a Bayesian model-learning framework the answer depends on the prior expectations of the dynamics of the model parameter that is to be inferred from the data. Local time constraints on the priors are insufficient to pick one interpretation over another. On the other hand, nonlocal time constraints, induced by a $1/f$ noise spectrum of the priors, is shown to permit learning of a specific model parameter even when there are infinitely many equally plausible interpretations of the data. This transition is inferred by a remarkable mapping of the model estimation problem to a dissipative physical system, allowing the use of powerful statistical mechanical methods to uncover the transition from indeterminate to determinate model learning.Comment: 8 pages, 2 figure

From classroom teaching to e-learning: the way for a strong definition

In any process of adoption of e-learning is important to understand his elements and the way they interrelate. This work tries to achieve the e-Learning definition using a graphical interpretation supported by mathematical language that helps the understanding, step-by-step, of the transition from “Classroom Learning” to “e Learning”. In the last step, the obtained graphic and formula is used in order to reach what we call the strong e Learning definition

SOM-VAE: Interpretable Discrete Representation Learning on Time Series

High-dimensional time series are common in many domains. Since human cognition is not optimized to work well in high-dimensional spaces, these areas could benefit from interpretable low-dimensional representations. However, most representation learning algorithms for time series data are difficult to interpret. This is due to non-intuitive mappings from data features to salient properties of the representation and non-smoothness over time. To address this problem, we propose a new representation learning framework building on ideas from interpretable discrete dimensionality reduction and deep generative modeling. This framework allows us to learn discrete representations of time series, which give rise to smooth and interpretable embeddings with superior clustering performance. We introduce a new way to overcome the non-differentiability in discrete representation learning and present a gradient-based version of the traditional self-organizing map algorithm that is more performant than the original. Furthermore, to allow for a probabilistic interpretation of our method, we integrate a Markov model in the representation space. This model uncovers the temporal transition structure, improves clustering performance even further and provides additional explanatory insights as well as a natural representation of uncertainty. We evaluate our model in terms of clustering performance and interpretability on static (Fashion-)MNIST data, a time series of linearly interpolated (Fashion-)MNIST images, a chaotic Lorenz attractor system with two macro states, as well as on a challenging real world medical time series application on the eICU data set. Our learned representations compare favorably with competitor methods and facilitate downstream tasks on the real world data.Comment: Accepted for publication at the Seventh International Conference on Learning Representations (ICLR 2019

Interpreting gains and losses in conceptual test using Item Response Theory

Conceptual tests are widely used by physics instructors to assess students' conceptual understanding and compare teaching methods. It is common to look at students' changes in their answers between a pre-test and a post-test to quantify a transition in student's conceptions. This is often done by looking at the proportion of incorrect answers in the pre-test that changes to correct answers in the post-test -- the gain -- and the proportion of correct answers that changes to incorrect answers -- the loss. By comparing theoretical predictions to experimental data on the Force Concept Inventory, we shown that Item Response Theory (IRT) is able to fairly well predict the observed gains and losses. We then use IRT to quantify the student's changes in a test-retest situation when no learning occurs and show that $i)$ up to 25\% of total answers can change due to the non-deterministic nature of student's answer and that $ii)$ gains and losses can go from 0\% to 100\%. Still using IRT, we highlight the conditions that must satisfy a test in order to minimize gains and losses when no learning occurs. Finally, recommandations on the interpretation of such pre/post-test progression with respect to the initial level of students are proposed

Robot introspection through learned hidden Markov models

In this paper we describe a machine learning approach for acquiring a model of a robot behaviour from raw sensor data. We are interested in automating the acquisition of behavioural models to provide a robot with an introspective capability. We assume that the behaviour of a robot in achieving a task can be modelled as a finite stochastic state transition system. Beginning with data recorded by a robot in the execution of a task, we use unsupervised learning techniques to estimate a hidden Markov model (HMM) that can be used both for predicting and explaining the behaviour of the robot in subsequent executions of the task. We demonstrate that it is feasible to automate the entire process of learning a high quality HMM from the data recorded by the robot during execution of its task.The learned HMM can be used both for monitoring and controlling the behaviour of the robot. The ultimate purpose of our work is to learn models for the full set of tasks associated with a given problem domain, and to integrate these models with a generative task planner. We want to show that these models can be used successfully in controlling the execution of a plan. However, this paper does not develop the planning and control aspects of our work, focussing instead on the learning methodology and the evaluation of a learned model. The essential property of the models we seek to construct is that the most probable trajectory through a model, given the observations made by the robot, accurately diagnoses, or explains, the behaviour that the robot actually performed when making these observations. In the work reported here we consider a navigation task. We explain the learning process, the experimental setup and the structure of the resulting learned behavioural models. We then evaluate the extent to which explanations proposed by the learned models accord with a human observer's interpretation of the behaviour exhibited by the robot in its execution of the task